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From Constant to Rough: A Survey of Continuous Volatility Modeling

Author

Listed:
  • Giulia Di Nunno

    (Department of Mathematics, University of Oslo, 0851 Oslo, Norway
    Department of Business and Management Science, NHH Norwegian School of Economics, 5045 Bergen, Norway)

  • Kęstutis Kubilius

    (Faculty of Mathematics and Informatics, Vilnius University, LT-03225 Vilnius, Lithuania)

  • Yuliya Mishura

    (Department of Probability, Statistics and Actuarial Mathematics, Taras Shevchenko National University of Kyiv, 01601 Kyiv, Ukraine
    Division of Mathematics and Physics, Mälardalen University, 722 20 Västerås, Sweden)

  • Anton Yurchenko-Tytarenko

    (Department of Mathematics, University of Oslo, 0851 Oslo, Norway)

Abstract

In this paper, we present a comprehensive survey of continuous stochastic volatility models, discussing their historical development and the key stylized facts that have driven the field. Special attention is dedicated to fractional and rough methods: without advocating for either roughness or long memory, we outline the motivation behind them and characterize some landmark models. In addition, we briefly touch on the problem of VIX modeling and recent advances in the SPX-VIX joint calibration puzzle.

Suggested Citation

  • Giulia Di Nunno & Kęstutis Kubilius & Yuliya Mishura & Anton Yurchenko-Tytarenko, 2023. "From Constant to Rough: A Survey of Continuous Volatility Modeling," Mathematics, MDPI, vol. 11(19), pages 1-35, October.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:19:p:4201-:d:1255656
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    References listed on IDEAS

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    9. Guido Gazzani & Julien Guyon, 2024. "Pricing and calibration in the 4-factor path-dependent volatility model," Papers 2406.02319, arXiv.org, revised Feb 2025.
    10. Pere Diaz-Lozano & Thomas K. Kloster, 2026. "A Wiener Chaos Approach to Martingale Modelling and Implied Volatility Calibration," Papers 2602.16232, arXiv.org.

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